Numerical Simulations of Galaxy Formation

Numerical Simulations of Galaxy Formation Matthias Steinmetz

arXiv:astro-ph/9608013v1 2 Aug 1996

Department of Astronomy, University of California, Berkeley, CA 94720, USA

Abstract. An overview over the current status of modeling galaxies by means of numerical simulations is given. After a short description of how galaxies form in hierarchically clustering scenarios, success and failures of current simulations are demonstrated using three different applications: the morphology of present day galaxies; the appearance of high redshift galaxies; and the nature of the Ly-α forest and metal absorption lines. It is shown that current simulations can qualitatively account for many observed features of galaxies. However, the objects which form in these simulations suffer from a strong overcooling problem. Star formation and feedback processes are likely to be indispensable ingredients for a realistic description even of the most basic parameters of a galaxy. The progenitors of todays galaxies are expected to be highly irregular and concentrated, as supported by recent observations. Though they exhibit a velocity dis∗ persion similar to present day L > ∼ L galaxies, they may be much less massive. The filamentary distribution of the gas provides a natural explanation for Ly-α and metal absorption systems. Furthermore, numerical simulations can be used to avoid misinterpretations of observed data and are able to alleviate some apparent contradictions in the size estimates of Ly-α absorption systems.

1

Introduction

Within the last two or three years, the advent of 10m class telescopes like the KECK and the superb imaging quality of the refurbished Hubble-SpaceTelescope (HST) have revolutionized the way we can look at the formation of galaxies. While a few years ago observations were restricted to galaxies which were at best a few billion years younger than the Milkyway, we can now routinely study galaxy formation at redshift z > 1, when galaxies were only 20% of their present age. And even the first billion years of the life of a galaxy seem to be reachable (Steidel et al. 1996). Though these observations are still in their childhood, we can expect that with the advent of several 8m class telescopes (including the VLT) we will construct a dense coverage of the morphologies of galaxies from today back to redshifts of z > 3. These observations are not only likely to provide important clues on the formation process of galaxies themselves, they will also constrain cosmological background models. Confronted with these detail-rich observations, however, theoretical models of galaxy formation, which mainly classify galaxies according to their Hubble type and therefore according to their global star formation history, seem to be outdated. Also so-called quasianalytic models which were successfully applied to the evolution of different populations of galaxies, e.g. to the Butcher-Oemler effect (Kauffmann 1995) and to the large scale distribution of galaxies (Kauffmann, Nusser & Steinmetz 1996)), say little about the spatial distribution of light

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within individual galaxies at different redshifts. Only highly resolved numerical simulation appear to be capable to provide the adequate theoretical framework for these new observations. In the following, I try to give a brief overview on the current status of studying galaxy formation by numerical simulation. Besides describing progress and failure in modeling current galaxy populations, I will also draw connections to the appearance of high redshift galaxies and the origin of Ly-α absorption lines.

2 Galaxy Formation in Hierarchically Clustering Universes Hierarchical clustering is at present the most successful theory of structure formation. In this scenario, structure grows as systems of progressively higher masses merge and collapse to form newly virialized systems. Over the last two decades, the build-up of the mass hierarchy has been investigated in detail by means of N-body simulations (for a review see, e.g., Davis et al. 1992). However in comparing the results of N-body simulations with observed galaxies, it seems unlikely that there is a very close correspondence between galaxies on the one hand side and the dark matter halos on the other. The circular velocity of a galaxy is not directly correlated to the circular velocity of a dark matter halo (Navarro, Frenk & White 1996), nor does each dark matter halo necessarily contain one and only one galaxy (see, for example, Kauffmann et al. 1996). Within the last few years, we have began to simulate the dynamical evolution of the baryonic component by including the effects of gas dynamics, shock heating and radiative cooling (for an overview, see e.g. Steinmetz, 1996a and references therein). First attempts to mimic the effects of star formations have been performed. Though many of the physical and numerical issues of these advanced simulations are still matter of debate, some qualitative features describing galaxy formation seem common in all of these simulations. The simulations presented below have been performed using the smoothed particle hydrodynamics code GRAPESPH (Steinmetz 1996b). They have a mass resolution of several 106 M⊙ and a spatial resolution of a few kpc. Using a multimass technique, the tidal field exerted by surrounding matter up to radii of 30 Mpc is included. In spite of their high resolution, the evolution of these galaxies is nevertheless followed up to the present epoch. The achieved numerical resolution therefore surpasses that of any other cosmological galaxy formation simulations performed so far by a factor of five or more. Details of the simulations themselves can be found in Navarro & Steinmetz (1996) and in Haehnelt, Steinmetz & Rauch (1996). Though the simulations were performed using the standard cold dark matter (CDM) cosmogony (i.e. , Ω0 = 1, h = 0.5, Λ = 0, σ8 = 0.63), many of the results are quite generic for any hierarchically clustering scenario. Furthermore, differences between different cosmological scenarios are partially eliminated due to the different normalizations: the normalization is usually chosen so to match the observed abundance of rich clusters (σ8 ≈ 0.63 Ω −0.6 ).

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3

Cooling, Mergers and the Morphology of Galaxies

While the build-up process of dark matter halos in hierarchically clustering scenarios is fairly well understood, the dynamics of the gaseous component is much less clear. It is usually assumed that most of the gas within a dark matter halo is able to cool radiatively. Due to the high cooling capabilities, no substantial gas pressure can be established and gas collapses until it settles in a rotationally supported disk. According to the tidal torque theory the gas can (marginally) acquire enough angular momentum to explain the size of todays disk galaxies (Fall & Efstathiou 1980). Mergers of disk galaxies (or their progenitors at higher redshift) provide a plausible explanation for the formation of ellipticals. This picture is indeed qualitatively supported by the outcome of numerical simulations as those presented at this conference: Halos which form in the field or in a filament typically experience a relatively quiescent merging history and no major merger is involved at redshifts smaller than about one. Within such a halo, the cooling gas settles and forms a rotationally supported disk. In a denser environment like a group of galaxies, a more violent merging history arises: During a major merger of two dark halos, the fusion of the two gaseous disks at the center of the dark matter halos ends up in a very compact, slowly rotating gas concentration. Simulations which include star formation (Katz 1992, Steinmetz & M¨ uller 1995) show that during such a merging event gas is efficiently transformed into stars and an ellipsoidal distribution of stars arises – a scenario for the formation of bulges and/or elliptical galaxies. However, though the general picture seem to be pretty promising, a closer look at these galaxy-like objects exhibit quite substantial differences to observed galaxies: First of all it has still to be shown that the right fraction of elliptical to spiral (as a function of the environment) can be achieved. This also may critically depend on the cosmological background model. Furthermore, though the arising objects visually represent spiral galaxies, they are far too concentrated. In contrast to the assumption of Fall & Efstathiou (1980) the gas has not been accreted axisymmetricly but by a series of merging events. Consequently angular momentum is efficiently transported from the gas to the dark matter halo (Navarro, Frenk & White, 1995) and the specific angular momentum of the gaseous object is only 10 to 20 per cent of that of the dark halo. A more detailed analysis (Navarro & Steinmetz 1996) demonstrates that gas which falls in diffusely (and also less bound gas lumps which are tidally disrupted early on) settles down to form a disk. However, most of the gas lumps are sufficiently tightly bound to resist the tidal field of the halo. They spiral down to the center due to dynamical friction and deliver most of their angular momentum to the dark halo. The numerical models predict the formation of disks, as observed, but far too much mass is acquired by the central “bulge”. Note that this is an immediate consequence of the cooling catastrophe (White & Rees 1978, Blanchard, VallsGabaud & Mamon 1992) and the neglect of feedback processes. Since cooling times scale inversely with density, the dissipative collapse of gas is more efficient at high redshift because the dark matter halos present at that time (and the universe as a whole) were denser.

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Up to the present, there has been no self–consistent high–resolution simulation which avoids the angular momentum problem. In order to solve it, one has to take care that more gas is diffusely accreted. A variety of different physical processes which might be able to solve this problem are currently under discussion: 1. One possibility is to change the merging history of the forming galaxy, e.g. by using a fluctuation spectrum with less power on small scales as predicted, for example, by a cosmogony with hot and cold dark matter. Changing the cosmological parameters Ω0 , Λ0 has probably rather little influence: Although the merging rate in the near past can be changed a lot, the merging history, expressed in terms of number of mergers and mass distribution of progenitors, is quite similar (Lacey & Cole 1993). However, it still has to be investigated to what extend the non-linearity of the merger process itself affects the result. For example, low Ω models typically have a higher baryon fraction and, therefore, self gravitation of the gas component may be more important and may reduce the efficiency of the angular momentum transport. 2. A photoionizing UV background with a strength as required to explain the Ly-α forest (see below) may suppress the formation of small structures (vc < ∼ 50 km/sec, Efstathiou 1992) and gas might fall in more diffusely. Therefore, the angular momentum transport to the halo might be reduced. However, the simulations presented here are only slightly influenced by the UV background: Most of the central gas clump has formed at sufficiently high redshifts (i.e. at sufficiently high densities) that recombination (∝ ̺2 ) dominates over photoionization (∝ ̺). 3. A realistic galaxy formation model has to include the effects of star formation, and the solution of the angular momentum problem is most likely related to feedback due to supernova and stellar winds. First simulations which account for feedback due to star formation (Katz 1992) assume that supernovae increase the thermal energy of the surrounding gas. Most of this energy, however, is immediately radiated away due to the high cooling capability of the gas. As a result, the formation of small lumps of gas cannot be prevented. The main influence of star formation is to transform a dense knot of gas into a slightly more diffuse lump of stars, but the extensive transport of angular momentum to the dark halo has not been overcome. It is conceivable that momentum input due to supernovae might have a much stronger effect (Navarro & White 1993).

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The Appearance of High Redshift Galaxies

Recently, Steidel and coworkers (1996, see also the contributions of Giavalisco and Macchetto to this conference) have detected and spatially resolved galaxies at redshifts z > 3. These galaxies appear to be very compact and often show substantial substructure. In case of a high Ω0 universe, these objects seem to be at least half as abundant as L∗ galaxies today. It has been argued that

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Fig. 1. The distribution of gas projected in the X-Y and Y-Z plane shown for 6 different redshifts. The gas infall is mainly lumpy. Diffusely infalling gas settles down to form a rotationally supported disk.

the equivalent width of saturated absorption lines implies velocities dispersions for these galaxies of the order of 180-320 km/sec, though it is still matter of debate whether these velocity dispersions are gravitational. By comparing with the expected number densities of dark matter halos with velocity dispersions higher than 180 km/sec, Mo & Fukujita (1996) argued that this observation can be used to rule out some cosmological scenarios. Contrary to some recent claims, size, abundance and substructure of these objects are consistent with most structure formation scenarios, and by parts even predicted (see, e.g. , Katz 1992). To demonstrate that, figure 2a shows an artificial I-band CCD image of a galaxy at redshift 3.1 as it forms in the numerical simulations presented above. The picture has been created by translating the ages of the formed star particles into I band luminosities using spectrophoto-

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metric models (Contardo, Steinmetz & Fritze-von Alvensleben, in preparation). A point spread function similar to that of the HST has been assumed. No assumptions on noise and absorption due to intervening dust have been done. The object exhibits a total apparent luminosity of mI = 22.5, the central surface brightness is µI = 20. Analyzing the velocity dispersion of the system, typical values of 200 km/sec can be found, while the halo circular velocity is about 30 per cent smaller. The total mass of the object is less than about 20 per cent of that of the corresponding object at the present epoch, though the circular velocity is similar. Comparing these objects with the corresponding galaxies at the present epoch, the early formed stars can be dominantly found close to the center and may correspond to the formation of (or parts of) the bulge component. However, most of the mass of the galaxy at z = 0 is not yet collapsed but is dispersed over a few hundred kpc, partially concentrated in several less massive subclumps. The high velocity dispersion of the progenitors may be surprising, but it is easily understandable in the context of hierarchical clustering scenarios. In figure 2b, the circular velocity and in figure 2c the mass of the most massive progenitor of halos with circular velocities between 80 and 200 km/sec at z = 0 is shown, normalized to the mass and circular velocity at the present epoch, respectively. Going to higher redshifts, one can see that the circular velocity is rising up to redshifts of about 2, though the mass is decreasing by more than a factor of 3. Only at redshift close to 4, mass and circular velocity are rapidly dropping. The rise of circular velocity can be understood as following (for the sake of simplicity of the argument, Ω = 1 and h = 0.5 has been assumed): for a given circular velocity vc , the mass within the virial radius (i.e. the radius within which the average overdensity is 178 times the critical density) is given by M (vc , z) = 4 1012 (

vc )3 (1 + z)−1.5 , 200km/sec

(1)

i.e. for a constant circular velocity, an object at higher redshift has a lower mass, but also a correspondingly smaller virial radius. According to the Press-Schechter algorithm, an object of mass M has on average acquired half of its mass at a “formation” redshift of  −(n+3)/6 p M (n+3)/3 zf = 2 −1 , (2) M∗ n being the spectral index of the power spectrum (for CDM, it is n ≈ −1 . . . − 2 on scales of galaxies). M∗ is the typical non-linear mass scale. Normalizing a CDM like power spectrum to cluster abundances, we obtain M ∗ = 4 1013 (1 + z)−6/(3+n) M⊙

(3)

(White 1996). By comparing equations 1 and 2, the circular velocity √ at the formation redshift is larger as long as M (vc , z) > Cn M ∗ (z), with Cn = ( 2(3+n)/3 − 1/ (22/3 − 1))6/(3+n) . For typical values of the spectral index n on scales of galaxies, Cn ≈ 0.5 . . . 2. The circular velocities of high redshift galaxies, are expected to

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drop only if M (vc , z) ≫ M ∗ (z). Their inferred abundance being similar to todays galaxies (namely L∗ ) therefore implies that these galaxies (or at least their halos) would have roughly the same circular velocities as today galaxies (namely about 200 km/sec), though their mass is much smaller (a factor of 10). This also reflects another feature seen in N-body simulations, namely that as long a ∗ M (vc , z) < ∼ M (z), every dark matter also has a well defined progenitor at higher redshifts, while if M (vc , z) ≫ M ∗ (z), the object has been formed by merging several objects of comparable mass. Concerning the abundances of these objects, one also has to keep in mind the weak correlation between the actual circular velocity of a galaxy and the circular velocity of a dark matter halo, as mentioned above: First of all, the maximum of the circular velocity can be up to 40 per cent higher (Navarro, Frenk & White, 1996) and it is achieved at radii much smaller than the virial radius. Secondly, as the baryons accumulate near the center of the galaxies the depth of the potential well is further increased. This implies that the circular velocity of dark matter halos is likely to be (substantially) smaller than that of the observed galaxy. Since their circular velocity is smaller, they are more abundant. Constraints derived via the Press-Schechter algorithm are likely less severe than they seem to be on the first view. Similar caveats also hold using the abundance of damped Ly-α systems to constrain cosmological models.

Fig. 2. Left: Artificial I-band CCD image of a z=3 galaxy as formed in a CDM simulation. The image is 7.5 arcsec across; Middle: mass of the most massive progenitor at redshift z normalized to the halo mass at z = 0; Right: circular velocity of the most massive progenitor at redshift z normalized to the circular velocity at z = 0.

5

Ly-α Absorbers and Metal Line Systems

Considering the difficulties if implementing models of star formation, and, therefore, of modeling the light emitted by galaxies, it is an intriguing alternative to study the absorption characteristics of the gas. This exercise has been successfully performed within the last two years (Cen et al. 1994, Petitjean et al. 1995, Hernquist et al. 1996, Haehnelt et al. 1996). It seems that the gas distribution as seen in large scale structure simulations can account for the large dynamic range of column densities seen in Ly-α absorption systems, from column densities of a few 1013 cm−2 up to 1020 cm−2 or higher. Very low column density systems

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Fig. 3. HI and CIV absorption as produced by the numerical simulations for lines-of-sight of different column densities. HI and CIV are shifted relative to each other by 0.5. Only λ1538 line of the CIV doublet is shown.

(1013 cm−2 ) typically arise for light rays penetrating voids, higher column densities arise if filaments (1015 cm−2 ) or even individual gaseous halos (> 1017 cm−2 ) are penetrated. Typical absorption lines as they are produced in numerical simulations are shown in figure 3. Sometimes, these systems do not even represent physically connected systems, but are caustics in the velocity space. Matching the column density distribution to observations, however, requires adjustment of the ratio J21 /nb by about a factor of ≈ 1/3 from standard values. −3 −3 The low physical density (n < ∼ 10 cm ) in systems with column densities 16 −2 less than about 10 cm also implies that the cooling time scales for the gas can be similar or even larger than the local dynamical time scales. Therefore, substantial deviation of the actual gas temperature from the photoionization equilibrium temperature can arise. Due to the rather strong temperature dependence of the ionization state of hydrogen, carbon and other relevant metals, the assumption of photionization temperatures leads in many cases to errors in the determination of total density and ionization fractions. For example a modest change in the temperature by a factor of two can change the CII/CIV ratio by an order of magnitude and the line-of-sight extent of CIV absorption systems inferred from photoionization models depends very strongly on the actual temperature (Haehnelt, Rauch & Steinmetz 1996). For more details on metal absorption systems see the contribution of Haehnelt in this volume.

6

Summary and Conclusions

Numerical simulations are likely the only way to model galaxy formation which can account for the detail-rich appearance of galaxies at low and high redshifts

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as it is expected (and partially already seen) by observations using the new generations of 8m class telescopes. From this point of view, the outcome of current numerical simulations on the formation of galaxies in hierarchically clustering scenarios has been presented, specifically the morphology of present galaxies, the appearance of high redshift galaxies and the origin of the Ly-α forest and metal absorption lines. It is encouraging that the same simulation, which was designed to study the properties of present galaxies, allows at least qualitatively to understand a large variety of features seen in objects at different redshifts. However, the simulations only follow the evolution of individual galaxies and demonstrate that the investigated scenario is potentially able to explain different morphological types at different redshifts. It is still to be shown that also the statistical behavior of a galaxy population as a whole can be reproduced. Furthermore, the simulations exhibit problems in the hierarchically clustering picture, which require further investigation. The most prominent problem is the overcooling and the related overly small angular momentum of disk galaxies. The solution of these problems is likely related to feedback processes due to stellar evolution, like, e.g. supernovae and stellar winds.

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